get this gradient style in blender
Gradient texture is your friend:
https://blender.stackexchange.com/a/49351/88382

You can also play with lights, since it seems that in one of the reference images the colors of the metaballs come from colored lights.

(if you need to have a single objects instead many objects you can join them. I think that metaballs btw are considered a single object in blender, so the colors are applied to the full object, not to the single meta-primitives - so please share screenshot or blend file to fully understand the problem)